Train Scheduling Problem with Consideration of Praying Constraint as anApplication of Job Shop Scheduling Problem

The present paper extends the idea of job shop scheduling problem with resting constraints to the trainscheduling problem with the Muslim praying considerations. For this purpose, after proposing the newmathematical model, a heuristic algorithm based on the Electromagnetism-Like algorithm (EM) whichis well adjusted to scheduling problems is employed to solve the large-size practical cases. Theeffectiveness of the proposed algorithm is then validated by comparing with optimum solution usingsmall-size instances and simulated annealing algorithm, and Particle swarm Optimization (PSO) usingmedium and large-size instances. At the end, a practical case from Iranian railway network is studiedand the results are reported. The results indicate that in the case of considering the Muslim prayingconstraint, the ratios of total tardiness of trains, and the total praying times are 14.5%, and 3.5%,respectively, while in the case of relaxing this constraint; the first ratio reduces to 12.3%. This resultdemonstrates that the proposed algorithm is able to schedule the praying times so that in many casesthe trains with different directions meet each other during the praying time